A certified basis of 4 identities

This list of identities is a basis, proved in Lean, of 4 semigroups of order six, all of which generate the variety V[5553]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-492965db4dec03dc in the data of the bases-min seal.

Certified for

[6, 5553] [6, 5563] [6, 9546] [6, 9657]

The identities

x³ ≈ x⁴
x²y ≈ xyx
x³y ≈ x²y
xy² ≈ xy³